Is it true that |b - 2| + |b + 8| = 10 ?

C.

These type of questions, it is much faster if you realize the critical points of the equation. In this case, critical points are b=2 and b=-8.
From this, you know that there are three intervals that the equation must satisfy.

A interval: b<-8
B interval: -8<b<2
C interval: b>2

If you find that b fall into one of these interval, then it must be right. (1) doesn't since it falls into intervals A and B, so INSUFFICIENT. (2) doesn't either because it falls into interval B and C, INSUFFICIENT. Together, it falls into interval B. SUFFICIENT.

I am not sure how C could be correct..

There are only 2 possible values of B that could satisfy the equation

|b-2|+|b+8|=10 , B is either2 or -8

Combining C

b<2>=-8


Combining both


B could have a value between -8......2 ?

Why are we not considering the values between ?
Thanks for clarrifying..

|b-2|+|b+8|=10

Plug in any number between -8 and 2 will satisfy the equation.

C.

These type of questions, it is much faster if you realize the critical points of the equation. In this case, critical points are b=2 and b=-8.
From this, you know that there are three intervals that the equation must satisfy.

A interval: b<-8
B interval: -8<b<2
C interval: b>2

If you find that b fall into one of these interval, then it must be right. (1) doesn't since it falls into intervals A and B, so INSUFFICIENT. (2) doesn't either because it falls into interval B and C, INSUFFICIENT. Together, it falls into interval B. SUFFICIENT.


*Additional comment: for this method to be useful, you should at least plug in a value from those interval to see if which one equals 10.

(C) for me too

|b-2|+|b+8|=10

I suggest to analyse quickly what is going on by replacing the absolutes.

o If b < -8 then
|b-2|+|b+8|
= -(b-2) - (b+8)
= -2*b - 6 >>> Not 10 and could not be

o If -8 =< b =< 2 then
|b-2|+|b+8|
= -(b-2) + (b+8)
= 10 >>> Sounds good

o If b > 2 then
|b-2|+|b+8|
= +(b-2) + (b+8)
= 2*b + 6 >>> Not 10 and could not be

From 1
b <= 2 >>>> So, we cannot conclude as it could be that -8 =< b =< 2 or b < -8

INSUFF.

From 2
b >= -8 >>>> So, we cannot conclude again as it could be that -8 =< b =< 2 or b > 2.

INSUFF.

Both (1) & (2)
Bongo.... It's -8 =< b =< 2 and we have seen that |b-2|+|b+8| = 10.

SUFF.

If I can only freakin add on D day..arrrgggggggh...

guys any suggestions on how to avoid such mistakes????

It happens to me too when I try to do it too fast or do it at work. I suggest writing it out step by step or get a good sleep. Or maybe it is just rainy today :D

Asked: Is it true that |b - 2| + |b + 8| = 10 ?
-8---------b------------2
For \(-8 \leq b \leq 2\)
|b-2|+|b+8| = 10

(1) b less than or equal to 2
If b is greater than or equal to -8
|b-2|+|b+8| = 10
Otherwise NOT
NOT SUFFICIENT

(2) b is greater than or equal to negative 8
If b less than or equal to 2
|b-2|+|b+8| = 10
Otherwise NOT
NOT SUFFICIENT

(1) + (2)
(1) b less than or equal to 2
(2) b is greater than or equal to negative 8
For \(-8 \leq b \leq 2\)
|b-2|+|b+8| = 10
SUFFICIENT

IMO C

When you read statement 1, it seems sufficient. Fair enough.

When you read statement 2, you might want to check for b=-9.
\(11+1=12\) which is not equal to 10. That means we need statement 2 as well.

Hence C

Thank you!

Hi,

When solving for questions where you have two absolute values added to each other, the best way is to work with distances traveled on the number line.

The absolute value is defined as the distance traveled from the origin on the number line, so if |x - 2| = 5, this means that the distance traveled from the origin i.e. 2 has to be 5 units. Imagine a person standing at 2 on the number line and having to travel a distance of 5 units from 2. The person can move left to a distance of 5 units and will end up at -3 or he can move right to a distance of 5 units and will end up at 7. These would be the solutions to the equation |x - 2| = 5.

Now let us use this basic understanding to solve the question given.

|b - 2| + |b + 8| = 10

The question says that the total distance traveled from 2 to -8 is 10 units. So if we imagine two people, one who is at 2 and the other who is at -8 the total distance that needs to be covered by both together is 10 units. So the only way this can be done is if both of them meet art any point in between 2 and -8.

So the question just asks us if b is between -8 and 2.



Statement 1 and Statement 2 together give us this.

Answer: C

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